NEW YORK, June 6 (Reuters) - Oil prices jumped more than 2% on Thursday, reversing course after falling to near five-month lows in the previous session, following a report that the United States could postpone tariffs on Mexico.

Brent crude futures settled at $61.67 a barrel, gaining $1.04, or 1.7%. U.S. West Texas Intermediate crude futures settled at $52.59 a barrel, up 91 cents, or 1.8%. The benchmarks both rallied more than 2% in post-settlement trade.

U.S. stocks, which oil prices tend to follow, spiked after Bloomberg News reported the United States is considering a delay in the tariffs as talks continue.

"There's talk now that the U.S. might not put on the Mexico tariffs, and that's pushed equities up, and you've got a little bit of short covering based on that statement," said Dominick Chirichella, director of risk management and advisory services at EMI DTN in New York.

Prices had been near flat most of the session as sentiment remained dim on fresh signs of a stalling global economy and ongoing concerns about U.S. crude supply growth.

On Wednesday, Brent and WTI hit their lowest levels since mid-January at $59.45 and $50.60, respectively, after U.S. crude production hit a new record high and stockpiles hit their highest since July 2017.

Both Brent and U.S. crude are in bear-market territory, having lost more than 20% from peaks reached in late April.

Signals of slowing global economic activity have increased in recent months, fueled by trade tensions between the United States and China, the world's top two energy consumers.

U.S. President Donald Trump, in his latest public comments about the trade war, said he would likely decide on more China tariffs at the end of June, which followed his overnight threat to put tariffs on "at least" another $300 billion worth of Chinese goods.

Prices rallied strongly in the first five months of the year to a high of nearly $75 a barrel, supported by supply curbs by the Organization of the Petroleum Exporting Countries and some allies including Russia. Supply has also been limited by U.S. sanctions on oil exports from Iran and Venezuela.

Members of the OPEC+ group are set to discuss whether to extend their supply curbs further later this month.

President Vladimir Putin said on Thursday that Russia had differences with OPEC over what constituted a fair price for oil but said Moscow would take a joint decision with OPEC colleagues on output at a policy meeting in the coming weeks.